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Pareto efficient combinatorial auctions: Dichotomous preferences without quasilinearity

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  • Malik, Komal
  • Mishra, Debasis

Abstract

We consider a combinatorial auction model where preferences of agents over bundles of objects and payments need not be quasilinear. However, we restrict the preferences of agents to be dichotomous. An agent with dichotomous preference partitions the set of bundles of objects as acceptable and unacceptable, and at the same payment level, she is indifferent between bundles in each class but strictly prefers acceptable to unacceptable bundles. We show that there is no Pareto efficient, dominant strategy incentive compatible (DSIC), individually rational (IR) mechanism satisfying no subsidy if the domain of preferences includes all dichotomous preferences. However, a generalization of the VCG mechanism is Pareto efficient, DSIC, IR and satisfies no subsidy if the domain of preferences contains only positive income effect dichotomous preferences. We show tightness of this result: adding any non-dichotomous preference (satisfying some natural properties) to the domain of quasilinear dichotomous preferences brings back the impossibility result.

Suggested Citation

  • Malik, Komal & Mishra, Debasis, 2021. "Pareto efficient combinatorial auctions: Dichotomous preferences without quasilinearity," Journal of Economic Theory, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:jetheo:v:191:y:2021:i:c:s0022053120301216
    DOI: 10.1016/j.jet.2020.105128
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    2. Ryosuke Sakai & Shigehiro Serizawa, 2023. "Strategy-proof mechanism design with non-quasi-linear preferences: ex-post revenue maximization for an arbitrary number of objects," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(1), pages 103-120, January.
    3. Zhou, Yu & Serizawa, Shigehiro, 2023. "Multi-object auction design beyond quasi-linearity: Leading examples," Games and Economic Behavior, Elsevier, vol. 140(C), pages 210-228.
    4. Brandl, Florian & Peters, Dominik, 2022. "Approval voting under dichotomous preferences: A catalogue of characterizations," Journal of Economic Theory, Elsevier, vol. 205(C).
    5. Tomoya KAZUMURA, 2020. "When can we design efficient and strategy-proof rules in package assignment problems?," Discussion papers e-21-008, Graduate School of Economics , Kyoto University.
    6. Tierney, Ryan, 2022. "Incentives And Efficiency In Matching With Transfers: Towards Nonquasilinear Package Auctions," Discussion Papers on Economics 6/2022, University of Southern Denmark, Department of Economics.
    7. Yeu-Shiang Huang & Min-Sheng Yang & Jyh-Wen Ho, 2022. "Bundling Decisions for Selling Multiple Items in Online Auctions," Decision Analysis, INFORMS, vol. 19(1), pages 44-62, March.

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    More about this item

    Keywords

    Combinatorial auctions; Non-quasilinear preferences; Dichotomous preferences; Single-minded bidders;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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